Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int( input() )

def f( n ):
    return ( n*( n+1 )//2 )

memo = {}
i=1
limit = 10**9
while True:
    tmp = f(i)
    if tmp > limit:
        break
    memo[tmp] = 1
    i += 1

for i in memo:
    if i > n:
        break
    if n-i in memo:
        print( "YES" )
        exit(0)

print( "NO" )